Back to: Freshman Courses
0
Explanations
Questions
Chapter Two: Basic Concepts of Logic
🤔 Learning Appetizer
Imagine two people arguing: one says, “All Ethiopians are hardworking, so Abebe must be too.” The other replies, “But Abebe skips class and never studies!” Who is reasoning correctly?
Logic gives us tools to evaluate such arguments—not by opinion, but by structure and evidence. As C.S. Layman said: “Logic sharpens and refines our natural gifts to think, reason, and argue.” 🔍
2.1. What is Logic?
Etymology:
The word “logic” comes from the Greek “logos”, meaning sentence, discourse, reason, truth, or rule.
The word “logic” comes from the Greek “logos”, meaning sentence, discourse, reason, truth, or rule.
Formal Definition:
Logic is the science that evaluates arguments. It develops methods and principles to assess whether premises adequately support conclusions.
Logic is the science that evaluates arguments. It develops methods and principles to assess whether premises adequately support conclusions.
Logic is not about winning arguments—it’s about truth-preserving reasoning. It teaches us to:
• Construct sound arguments,
• Detect fallacies (errors in reasoning),
• Distinguish evidence from mere opinion.
Why Study Logic?
• In law: to build court cases.
• In science: to design experiments.
• In daily life: to avoid scams, propaganda, and misinformation.
Logic is the immune system of the mind—it protects against bad reasoning! 🛡️
• In law: to build court cases.
• In science: to design experiments.
• In daily life: to avoid scams, propaganda, and misinformation.
Logic is the immune system of the mind—it protects against bad reasoning! 🛡️
2.2. What is an Argument?
Argument (Logical Sense):
A group of statements where one or more premises claim to support a conclusion.
A group of statements where one or more premises claim to support a conclusion.
Key Clarifications:
- ❌ NOT a verbal fight (“They had an argument”).
- ✅ IS a structured reasoning process (“Their argument is valid”).
2.2.1. Statements, Premises, and Conclusions
A statement is a declarative sentence that is either true or false (e.g., “Mekelle is in Tigray” ✅; “Ethiopia was colonized by Germany” ❌).
Non-statements include questions, commands, and exclamations (e.g., “Close the door!”).
Every argument has:
• Premise(s): Evidence or reasons (e.g., “All mammals breathe air”).
• Conclusion: Claim supported by premises (e.g., “Whales breathe air”).
Example Argument:
• Premise 1: All Ethiopians are Africans.
• Premise 2: Tsionawit is Ethiopian.
• Conclusion: Therefore, Tsionawit is African.
→ This is a good argument—the premises necessitate the conclusion.
• Premise 1: All Ethiopians are Africans.
• Premise 2: Tsionawit is Ethiopian.
• Conclusion: Therefore, Tsionawit is African.
→ This is a good argument—the premises necessitate the conclusion.
2.2.2. Identifying Premises and Conclusions
Use indicator words:
- Conclusion Indicators: therefore, thus, hence, so, consequently.
→ “Socrates is mortal. Therefore, he will die.” - Premise Indicators: because, since, for, given that.
→ “She’s failing because she never studies.”
⚠️ If no indicators exist, ask: “What is the main claim?” That’s the conclusion.
2.3. Recognizing Arguments vs. Non-Arguments
Not all multi-sentence passages are arguments! An argument must:
1. Claim to present evidence (premises),
2. Claim that evidence supports a conclusion (inferential claim).
Common Non-Argumentative Passages:
- Warnings: “Don’t share political secrets with your spouse!” (No evidence → no argument).
- Advice: “You should study harder.” (Recommendation, not proof).
- Reports: “The Grand Renaissance Dam employs 13,000 Ethiopians.” (Facts without inference).
- Explanations: “Cows digest grass because they have special enzymes.”
→ Here, “Cows digest grass” is an accepted fact; the rest explains why.
→ In an argument, the conclusion would be disputed (e.g., “Cows digest grass, so they’re herbivores”). - Illustrations: “Elements have formulas: oxygen is O₂, water is H₂O.”
→ Shows how, not proves. But if it says, “Not all cancers are fatal—for example, basal cell carcinoma rarely kills,” it becomes an argument from example. - Conditional Statements: “If you study, you’ll pass.”
→ This is not an argument—it’s a single statement about a relationship.
→ But it can be part of an argument:
• Premise: You studied.
• Premise: If you study, you’ll pass.
• Conclusion: You’ll pass.
2.4. Types of Arguments: Deductive vs. Inductive
Deductive Argument:
Premises claim to support the conclusion with strict necessity.
→ If premises are true, the conclusion must be true.
Premises claim to support the conclusion with strict necessity.
→ If premises are true, the conclusion must be true.
Inductive Argument:
Premises claim to support the conclusion with probability.
→ If premises are true, the conclusion is likely (but not guaranteed).
Premises claim to support the conclusion with probability.
→ If premises are true, the conclusion is likely (but not guaranteed).
2.4.1. Deductive Arguments
Key Forms:
- Mathematical Reasoning: “2 apples + 3 bananas = 5 fruits.” (Necessary truth).
- Definitions: “Kebede is a physician; therefore, he is a doctor.” (Follows from meaning).
- Categorical Syllogism:
• All Ethiopians love their country.
• Debebe is Ethiopian.
• ∴ Debebe loves his country. - Hypothetical Syllogism:
• If you study, you’ll graduate.
• If you graduate, you’ll get a job.
• ∴ If you study, you’ll get a job. - Disjunctive Syllogism:
• Rewina is Ethiopian or Eritrean.
• She’s not Eritrean.
• ∴ She’s Ethiopian.
2.4.2. Inductive Arguments
Key Forms:
- Prediction: “Dark clouds are forming; it’ll rain soon.” (Past → future).
- Argument from Analogy:
“Computer A is fast. Computer B has the same specs. ∴ Computer B is fast.” - Generalization:
“3 of 4 prisoners surveyed are Black. ∴ 75% of prisoners are Black.” - Authority:
“Prof. X says quarks exist. ∴ Quarks exist.” (Relies on expert credibility). - Signs:
“There’s a ‘No Parking’ sign. ∴ Parking is prohibited.” - Causal Inference:
• Cause → Effect: “Water left in freezer → it froze.”
• Effect → Cause: “Chicken is dry → it was overcooked.”
Critical Distinction:
Deductive: “All birds fly. Penguins are birds. ∴ Penguins fly.” → Invalid (premise false).
Inductive: “Most birds fly. Penguins are birds. ∴ Penguins probably fly.” → Weak (ignores penguin exception).
→ Both can be logically flawed even with true premises!
Deductive: “All birds fly. Penguins are birds. ∴ Penguins fly.” → Invalid (premise false).
Inductive: “Most birds fly. Penguins are birds. ∴ Penguins probably fly.” → Weak (ignores penguin exception).
→ Both can be logically flawed even with true premises!
2.5. Evaluating Arguments
2.5.1. Deductive Arguments: Validity and Soundness
Validity: If premises are true, the conclusion must be true.
→ Depends only on logical structure, not truth of premises.
→ Depends only on logical structure, not truth of premises.
Validity ≠ Truth:
| Premises | Conclusion | Valid? |
|---|---|---|
| True | True | ✅ or ❌ |
| True | False | ❌ Always invalid! |
| False | True | ✅ or ❌ |
| False | False | ✅ or ❌ |
Valid but Unsound:
• All birds are mammals. (False)
• All women are birds. (False)
• ∴ All women are mammals. (True)
→ Valid (structure is correct) but unsound (premises false).
• All birds are mammals. (False)
• All women are birds. (False)
• ∴ All women are mammals. (True)
→ Valid (structure is correct) but unsound (premises false).
Soundness = Validity + True Premises
→ Only sound deductive arguments guarantee true conclusions.
→ Only sound deductive arguments guarantee true conclusions.
2.5.2. Inductive Arguments: Strength and Cogency
Strength: If premises are true, the conclusion is probably true.
→ Like validity, but probabilistic.
→ Like validity, but probabilistic.
Cogency = Strength + True Premises
→ Additionally, premises must not ignore critical counterevidence.
→ Additionally, premises must not ignore critical counterevidence.
Strong but Uncogent:
• “80 of 100 apples tested were tasty. ∴ All 100 are tasty.”
→ Strong (large sample).
→ But if 1 rotten apple was removed before testing, it’s uncogent (ignores key evidence).
• “80 of 100 apples tested were tasty. ∴ All 100 are tasty.”
→ Strong (large sample).
→ But if 1 rotten apple was removed before testing, it’s uncogent (ignores key evidence).
💡 Final Reflection
Logic isn’t about memorizing rules—it’s about thinking clearly. In Ethiopia’s diverse society, where misinformation can divide communities, logic is a tool for truth, justice, and unity. As you analyze arguments, ask:
• Is the reasoning valid/strong?
• Are the premises true and complete?
→ Only then can you build or evaluate a good argument! ✨
12 Complex Questions – Chapter Two: Basic Concepts of Logic
Deeply Detailed Explanations for Freshman University Students | Based on Logic and Critical Thinking (Unit 1)
1. Which of the following best defines logic as a field of study?
A) The art of winning arguments
B) The science that evaluates arguments
C) The study of language structures
D) The history of philosophical ideas
B) The science that evaluates arguments
C) The study of language structures
D) The history of philosophical ideas
✅ Explanation:
Logic is defined as the organized body of knowledge that evaluates arguments. It focuses on distinguishing good (valid/strong) arguments from bad (invalid/weak) ones using systematic methods. Option A confuses logic with rhetoric; C and D describe linguistics and history of philosophy, respectively.
2. An argument must contain:
A) A verbal dispute between two people
B) At least one premise and one conclusion
C) Emotional appeals to be persuasive
D) Historical evidence to support claims
B) At least one premise and one conclusion
C) Emotional appeals to be persuasive
D) Historical evidence to support claims
✅ Explanation:
In logic, an argument is a structured set of statements where premises (evidence) are claimed to support a conclusion. It is not a fight (A), and need not involve emotion (C) or history (D). The core is inferential support.
3. Which of the following is NOT a statement?
A) Ethiopia is in Africa.
B) Close the door!
C) Water boils at 100°C.
D) All humans are mortal.
B) Close the door!
C) Water boils at 100°C.
D) All humans are mortal.
✅ Explanation:
A statement must be a declarative sentence with a truth value (true or false). Commands (B), questions, and exclamations lack truth value and cannot be premises or conclusions.
4. In the argument: “All mammals are warm-blooded. Whales are mammals. Therefore, whales are warm-blooded,” the conclusion is:
A) All mammals are warm-blooded.
B) Whales are mammals.
C) Whales are warm-blooded.
D) Mammals include whales.
B) Whales are mammals.
C) Whales are warm-blooded.
D) Mammals include whales.
✅ Explanation:
The conclusion is the statement claimed to follow from the premises. The word “therefore” signals that “whales are warm-blooded” is the conclusion. Premises provide the support.
5. The word “because” in an argument typically indicates:
A) A premise
B) A conclusion
C) A counter-argument
D) A definition
B) A conclusion
C) A counter-argument
D) A definition
✅ Explanation:
“Because” is a premise indicator. It introduces evidence (premise) that supports a claim (conclusion). For example: “It’s raining because the sky is cloudy” → Premise: sky is cloudy; Conclusion: it’s raining.
6. Which argument is deductive?
A) Most birds fly; penguins are birds; so penguins probably fly.
B) All squares are rectangles; this shape is a square; so it is a rectangle.
C) She’s been late three times; she’ll likely be late again.
D) The survey shows 80% support; so the policy is popular.
B) All squares are rectangles; this shape is a square; so it is a rectangle.
C) She’s been late three times; she’ll likely be late again.
D) The survey shows 80% support; so the policy is popular.
✅ Explanation:
A deductive argument claims its conclusion follows with necessity from the premises. In B, if premises are true, the conclusion must be true. A, C, and D use probability → inductive.
7. An inductive argument is strong if:
A) It has three or more premises
B) Its premises make the conclusion probable
C) It uses emotional language
D) It avoids counterexamples
B) Its premises make the conclusion probable
C) It uses emotional language
D) It avoids counterexamples
✅ Explanation:
A strong inductive argument is one where, if the premises are true, the conclusion is improbable to be false (i.e., highly probable). Strength is about the logical link, not quantity (A) or emotion (C).
8. A deductive argument is valid if:
A) All its premises are factually true
B) It is impossible for the premises to be true and the conclusion false
C) It persuades the audience
D) It contains the word “therefore”
B) It is impossible for the premises to be true and the conclusion false
C) It persuades the audience
D) It contains the word “therefore”
✅ Explanation:
Validity depends solely on the logical structure, not truth of premises. If the conclusion must follow from the premises, the argument is valid—even if premises are false (e.g., “All cats bark; Fido is a cat; so Fido barks” is valid but unsound).
9. A sound argument must be:
A) Valid and have true premises
B) Strong and have probable premises
C) Persuasive and well-structured
D) Inductive and cogent
B) Strong and have probable premises
C) Persuasive and well-structured
D) Inductive and cogent
✅ Explanation:
A sound argument is a valid deductive argument with all true premises. Soundness = validity + factual accuracy. Only deductive arguments can be sound (B and D describe inductive cogency).
10. Which argument is cogent?
A) A valid argument with false premises
B) A strong argument with false premises
C) A strong argument with all true premises
D) A weak argument with true premises
B) A strong argument with false premises
C) A strong argument with all true premises
D) A weak argument with true premises
✅ Explanation:
A cogent argument is the inductive equivalent of soundness: it must be strong (premises → probable conclusion) and have all true premises. Option C meets both criteria.
11. The argument form: “If P, then Q. P. Therefore, Q.” is called:
A) Disjunctive syllogism
B) Modus ponens
C) Modus tollens
D) Hypothetical syllogism
B) Modus ponens
C) Modus tollens
D) Hypothetical syllogism
✅ Explanation:
This is the classic modus ponens (affirming the antecedent), a valid deductive form. Example: “If it rains, the ground gets wet. It is raining. So the ground is wet.”
12. A single conditional statement (e.g., “If it rains, the ground gets wet”) is:
A) Always a valid argument
B) Always an inductive argument
C) Not an argument by itself
D) A cogent argument
B) Always an inductive argument
C) Not an argument by itself
D) A cogent argument
✅ Explanation:
A conditional statement alone lacks an inferential claim—it doesn’t assert that the antecedent *is* true, only that *if* true, the consequent follows. Thus, it’s not an argument. Arguments require at least one premise and a conclusion.